A228082 Numbers that are of the form k + sum of binary digits of k for some nonnegative integer k.

0, 2, 3, 5, 7, 8, 9, 10, 11, 12, 14, 16, 17, 19, 20, 22, 24, 25, 26, 27, 28, 29, 31, 33, 34, 35, 36, 38, 40, 41, 42, 43, 44, 45, 47, 49, 50, 52, 53, 55, 57, 58, 59, 60, 61, 62, 64, 65, 66, 67, 68, 69, 70, 72, 73, 74, 75, 76, 77, 79, 81, 82, 84, 85, 87, 89, 90

Offset: 1

Author

Antti Karttunen, Aug 09 2013

Keywords

• nonn
• base

Comments

Complement of A010061.

Obtained when A092391 is sorted and duplicates are removed.

The asymptotic density of this sequence is 1 - (1/8) * (Sum_{n>=1} 1/2^a(n))^2 = 1 - A242403 = 0.747339... - Amiram Eldar, Nov 28 2020

References

• Steven R. Finch, Mathematical Constants, Cambridge, 2003, Section 2.24, pp. 179-180.
• József Sándor and Borislav Crstici, Handbook of Number theory II, Kluwer Academic Publishers, 2004, Chapter 4, p. 384-386.
• G. Troi and U. Zannier, Note on the density constant in the distribution of self-numbers, Bolletino U. M. I. (7) 9-A (1995), 143-148.

Links

• Antti Karttunen, Table of n, a(n) for n = 1..8192
• G. Troi and U. Zannier, Note on the density constant in the distribution of self-numbers. II, Bollettino dell'Unione Matematica Italiana 2-A (1999), 397-399.
• Index entries for Colombian or self numbers and related sequences

Crossrefs

Numbers that occur to the right of the leftmost column of A228083. Positions of nonzeros in A228085. A superset of A228088.

Cf. also A227643, A005187, A230091, A230092, A227915, A242403.

The even terms are the first row of A350601.

Programs

Haskell

a228082 n = a228082_list !! (n-1)
a228082_list = 0 : filter ((> 0) . a228085) [1..]
-- Reinhard Zumkeller, Oct 13 2013

Mathematica

Table[n + Total[IntegerDigits[n, 2]], {n, 0, 100}] // Union (* Jean-François Alcover, Sep 03 2013 *)